document.write( "Question 1074179: Candace and Darryl are playing a game with piles of beans. On each player’s turn, they must remove at least one, but at most 7 beans from one of the piles. It is Candace’s turn and there are
\n" ); document.write( "two piles of beans with 25 and 27 beans in each. The winner is the player to take the last bean. What is Candace’s best move? \n" ); document.write( "

Algebra.Com's Answer #688897 by ikleyn(52851) $\"\"$ $\"About$

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document.write( "I think that Candace's best strategy (winning strategy) is to maintain the difference of 0 between the number of beans in two piles.\r\n" );
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document.write( "Following to this strategy, Candace's next (closest) step is to remove 2 beans from the 27-beans pile.\r\n" );
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document.write( "So, Candace will achieve his strategic goal at the first step, and after any step of his partner Candace can maintain the difference of 0.\r\n" );
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document.write( "By doing in this way, whichever number of beans will Darryl remove from one container, the same number of beans will Candace \r\n" );
document.write( "remove from the other container, maintaining the number of beans the same in both containers.\r\n" );
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document.write( "By doing in this way, he will FORCE Darryl to remove, finally, the last bean (or the last portion of beans) from one of \r\n" );
document.write( "the two containers at Darryl's current step. \r\n" );
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document.write( "Then Candace wins the game at his next (=last) turn removing the same number of  remaining beans from the other container.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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